//
// Copyright (c) 2019 harmony-one
//
// SPDX-License-Identifier: MIT
//

package iqc

var residues = []int{
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}

var sieve_info = []Pair{
	{17, 8},
	{19, 10},
	{23, 5},
	{29, 15},
	{31, 6},
	{37, 35},
	{41, 4},
	{43, 41},
	{47, 43},
	{53, 41},
	{59, 44},
	{61, 50},
	{67, 6},
	{71, 65},
	{73, 48},
	{79, 2},
	{83, 35},
	{89, 86},
	{97, 20},
	{101, 88},
	{103, 89},
	{107, 60},
	{109, 55},
	{113, 1},
	{127, 75},
	{131, 56},
	{137, 85},
	{139, 29},
	{149, 86},
	{151, 149},
	{157, 21},
	{163, 74},
	{167, 32},
	{173, 3},
	{179, 114},
	{181, 82},
	{191, 10},
	{193, 60},
	{197, 130},
	{199, 144},
	{211, 128},
	{223, 139},
	{227, 135},
	{229, 205},
	{233, 192},
	{239, 170},
	{241, 26},
	{251, 175},
	{257, 28},
	{263, 100},
	{269, 234},
	{271, 89},
	{277, 65},
	{281, 131},
	{283, 241},
	{293, 205},
	{307, 37},
	{311, 290},
	{313, 213},
	{317, 124},
	{331, 10},
	{337, 189},
	{347, 6},
	{349, 60},
	{353, 293},
	{359, 307},
	{367, 205},
	{373, 80},
	{379, 346},
	{383, 89},
	{389, 24},
	{397, 65},
	{401, 225},
	{409, 198},
	{419, 63},
	{421, 184},
	{431, 147},
	{433, 254},
	{439, 119},
	{443, 324},
	{449, 36},
	{457, 354},
	{461, 211},
	{463, 333},
	{467, 37},
	{479, 312},
	{487, 219},
	{491, 101},
	{499, 140},
	{503, 140},
	{509, 127},
	{521, 106},
	{523, 483},
	{541, 511},
	{547, 455},
	{557, 293},
	{563, 549},
	{569, 28},
	{571, 242},
	{577, 172},
	{587, 172},
	{593, 87},
	{599, 526},
	{601, 308},
	{607, 561},
	{613, 197},
	{617, 405},
	{619, 528},
	{631, 107},
	{641, 603},
	{643, 457},
	{647, 102},
	{653, 102},
	{659, 554},
	{661, 69},
	{673, 64},
	{677, 114},
	{683, 520},
	{691, 297},
	{701, 442},
	{709, 396},
	{719, 153},
	{727, 141},
	{733, 486},
	{739, 307},
	{743, 595},
	{751, 582},
	{757, 676},
	{761, 316},
	{769, 350},
	{773, 147},
	{787, 668},
	{797, 639},
	{809, 98},
	{811, 573},
	{821, 320},
	{823, 758},
	{827, 472},
	{829, 39},
	{839, 751},
	{853, 223},
	{857, 655},
	{859, 362},
	{863, 773},
	{877, 756},
	{881, 739},
	{883, 138},
	{887, 123},
	{907, 836},
	{911, 490},
	{919, 878},
	{929, 313},
	{937, 606},
	{941, 175},
	{947, 286},
	{953, 295},
	{967, 260},
	{971, 612},
	{977, 613},
	{983, 907},
	{991, 569},
	{997, 970},
	{1009, 556},
	{1013, 223},
	{1019, 877},
	{1021, 77},
	{1031, 364},
	{1033, 704},
	{1039, 18},
	{1049, 497},
	{1051, 79},
	{1061, 846},
	{1063, 1},
	{1069, 30},
	{1087, 251},
	{1091, 486},
	{1093, 467},
	{1097, 365},
	{1103, 134},
	{1109, 290},
	{1117, 184},
	{1123, 493},
	{1129, 524},
	{1151, 534},
	{1153, 704},
	{1163, 1033},
	{1171, 19},
	{1181, 701},
	{1187, 917},
	{1193, 790},
	{1201, 1141},
	{1213, 1066},
	{1217, 580},
	{1223, 823},
	{1229, 729},
	{1231, 1029},
	{1237, 661},
	{1249, 133},
	{1259, 1237},
	{1277, 1168},
	{1279, 1098},
	{1283, 732},
	{1289, 1167},
	{1291, 453},
	{1297, 787},
	{1301, 459},
	{1303, 518},
	{1307, 917},
	{1319, 29},
	{1321, 450},
	{1327, 1302},
	{1361, 58},
	{1367, 800},
	{1373, 353},
	{1381, 358},
	{1399, 512},
	{1409, 897},
	{1423, 651},
	{1427, 957},
	{1429, 1412},
	{1433, 1052},
	{1439, 1163},
	{1447, 457},
	{1451, 700},
	{1453, 91},
	{1459, 112},
	{1471, 126},
	{1481, 1155},
	{1483, 494},
	{1487, 432},
	{1489, 880},
	{1493, 797},
	{1499, 757},
	{1511, 1175},
	{1523, 201},
	{1531, 1097},
	{1543, 877},
	{1549, 876},
	{1553, 1092},
	{1559, 81},
	{1567, 282},
	{1571, 1009},
	{1579, 667},
	{1583, 1002},
	{1597, 287},
	{1601, 676},
	{1607, 865},
	{1609, 316},
	{1613, 1164},
	{1619, 892},
	{1621, 1455},
	{1627, 357},
	{1637, 1198},
	{1657, 729},
	{1663, 1113},
	{1667, 1476},
	{1669, 452},
	{1693, 1591},
	{1697, 1119},
	{1699, 1215},
	{1709, 143},
	{1721, 890},
	{1723, 1185},
	{1733, 1583},
	{1741, 1354},
	{1747, 413},
	{1753, 932},
	{1759, 1250},
	{1777, 1025},
	{1783, 1204},
	{1787, 1202},
	{1789, 1253},
	{1801, 1317},
	{1811, 1686},
	{1823, 267},
	{1831, 744},
	{1847, 341},
	{1861, 1676},
	{1867, 322},
	{1871, 1040},
	{1873, 1080},
	{1877, 1173},
	{1879, 1202},
	{1889, 1463},
	{1901, 213},
	{1907, 454},
	{1913, 1563},
	{1931, 131},
	{1933, 515},
	{1949, 19},
	{1951, 95},
	{1973, 525},
	{1979, 1120},
	{1987, 170},
	{1993, 1635},
	{1997, 446},
	{1999, 1788},
	{2003, 1569},
	{2011, 1903},
	{2017, 567},
	{2027, 1977},
	{2029, 888},
	{2039, 1487},
	{2053, 1474},
	{2063, 1244},
	{2069, 1806},
	{2081, 18},
	{2083, 3},
	{2087, 746},
	{2089, 836},
	{2099, 2077},
	{2111, 1030},
	{2113, 678},
	{2129, 796},
	{2131, 405},
	{2137, 415},
	{2141, 411},
	{2143, 1856},
	{2153, 1658},
	{2161, 41},
	{2179, 1038},
	{2203, 78},
	{2207, 2125},
	{2213, 863},
	{2221, 203},
	{2237, 551},
	{2239, 1524},
	{2243, 1999},
	{2251, 529},
	{2267, 585},
	{2269, 2004},
	{2273, 254},
	{2281, 180},
	{2287, 1394},
	{2293, 1699},
	{2297, 1315},
	{2309, 2087},
	{2311, 1911},
	{2333, 1898},
	{2339, 805},
	{2341, 228},
	{2347, 2175},
	{2351, 365},
	{2357, 298},
	{2371, 74},
	{2377, 350},
	{2381, 2134},
	{2383, 2071},
	{2389, 2036},
	{2393, 779},
	{2399, 2272},
	{2411, 1127},
	{2417, 937},
	{2423, 534},
	{2437, 455},
	{2441, 621},
	{2447, 530},
	{2459, 1372},
	{2467, 2370},
	{2473, 124},
	{2477, 427},
	{2503, 730},
	{2521, 1093},
	{2531, 642},
	{2539, 271},
	{2543, 1851},
	{2549, 1568},
	{2551, 1796},
	{2557, 130},
	{2579, 210},
	{2591, 1756},
	{2593, 1161},
	{2609, 1846},
	{2617, 869},
	{2621, 2192},
	{2633, 2509},
	{2647, 1230},
	{2657, 608},
	{2659, 406},
	{2663, 2364},
	{2671, 1104},
	{2677, 1032},
	{2683, 1143},
	{2687, 1041},
	{2689, 2610},
	{2693, 574},
	{2699, 2606},
	{2707, 2057},
	{2711, 1469},
	{2713, 1128},
	{2719, 1264},
	{2729, 2667},
	{2731, 931},
	{2741, 1093},
	{2749, 2384},
	{2753, 1537},
	{2767, 2303},
	{2777, 2730},
	{2789, 1763},
	{2791, 2478},
	{2797, 1204},
	{2801, 2246},
	{2803, 2289},
	{2819, 866},
	{2833, 2126},
	{2837, 2558},
	{2843, 219},
	{2851, 445},
	{2857, 1882},
	{2861, 1158},
	{2879, 1858},
	{2887, 583},
	{2897, 1016},
	{2903, 1040},
	{2909, 2051},
	{2917, 396},
	{2927, 1865},
	{2939, 1264},
	{2953, 2042},
	{2957, 2229},
	{2963, 2913},
	{2969, 155},
	{2971, 253},
	{2999, 2268},
	{3001, 1463},
	{3011, 1609},
	{3019, 467},
	{3023, 2596},
	{3037, 297},
	{3041, 2},
	{3049, 1208},
	{3061, 1136},
	{3067, 2208},
	{3079, 1579},
	{3083, 527},
	{3089, 44},
	{3109, 2485},
	{3119, 2957},
	{3121, 1905},
	{3137, 2454},
	{3163, 1496},
	{3167, 2116},
	{3169, 787},
	{3181, 2690},
	{3187, 2686},
	{3191, 1388},
	{3203, 2349},
	{3209, 2309},
	{3217, 1666},
	{3221, 1175},
	{3229, 539},
	{3251, 292},
	{3253, 3226},
	{3257, 921},
	{3259, 1992},
	{3271, 339},
	{3299, 1287},
	{3301, 1324},
	{3307, 610},
	{3313, 1116},
	{3319, 2531},
	{3323, 412},
	{3329, 2545},
	{3331, 2237},
	{3343, 2214},
	{3347, 3338},
	{3359, 2302},
	{3361, 188},
	{3371, 30},
	{3373, 2014},
	{3389, 2772},
	{3391, 1510},
	{3407, 806},
	{3413, 349},
	{3433, 1177},
	{3449, 342},
	{3457, 1849},
	{3461, 208},
	{3463, 2847},
	{3467, 150},
	{3469, 1993},
	{3491, 2005},
	{3499, 1513},
	{3511, 2998},
	{3517, 3225},
	{3527, 2427},
	{3529, 3450},
	{3533, 1766},
	{3539, 670},
	{3541, 168},
	{3547, 2100},
	{3557, 2596},
	{3559, 3322},
	{3571, 643},
	{3581, 1453},
	{3583, 1181},
	{3593, 2810},
	{3607, 732},
	{3613, 811},
	{3617, 1077},
	{3623, 2467},
	{3631, 2005},
	{3637, 2939},
	{3643, 3459},
	{3659, 817},
	{3671, 933},
	{3673, 2705},
	{3677, 2364},
	{3691, 318},
	{3697, 910},
	{3701, 2585},
	{3709, 2142},
	{3719, 2010},
	{3727, 492},
	{3733, 1636},
	{3739, 3335},
	{3761, 2610},
	{3767, 1768},
	{3769, 3406},
	{3779, 1361},
	{3793, 607},
	{3797, 738},
	{3803, 1957},
	{3821, 2310},
	{3823, 1199},
	{3833, 727},
	{3847, 896},
	{3851, 469},
	{3853, 3005},
	{3863, 2642},
	{3877, 3009},
	{3881, 2418},
	{3889, 1568},
	{3907, 627},
	{3911, 1877},
	{3917, 2937},
	{3919, 3106},
	{3923, 2152},
	{3929, 578},
	{3931, 429},
	{3943, 3734},
	{3947, 2509},
	{3967, 1669},
	{3989, 3466},
	{4001, 3512},
	{4003, 3069},
	{4007, 1024},
	{4013, 2928},
	{4019, 259},
	{4021, 954},
	{4027, 2352},
	{4049, 4046},
	{4051, 2761},
	{4057, 569},
	{4073, 1155},
	{4079, 3207},
	{4091, 1569},
	{4093, 3000},
	{4099, 3738},
	{4111, 1346},
	{4127, 2106},
	{4129, 2168},
	{4133, 4023},
	{4139, 4046},
	{4153, 1428},
	{4157, 48},
	{4159, 4015},
	{4177, 1604},
	{4201, 1792},
	{4211, 3954},
	{4217, 1896},
	{4219, 2014},
	{4229, 2424},
	{4231, 1529},
	{4241, 2816},
	{4243, 2028},
	{4253, 78},
	{4259, 3891},
	{4261, 3731},
	{4271, 3701},
	{4273, 2720},
	{4283, 3693},
	{4289, 1685},
	{4297, 285},
	{4327, 1466},
	{4337, 3813},
	{4339, 1148},
	{4349, 3088},
	{4357, 857},
	{4363, 2713},
	{4373, 3562},
	{4391, 3669},
	{4397, 4193},
	{4409, 4278},
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